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ENGI 1313 Mechanics I

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ENGI 1313 Mechanics I Lecture 26: 3D Equilibrium of a Rigid Body Schedule Change Postponed Class Friday Nov. 9 Two Options Use review class Wednesday Nov. 28 ... – PowerPoint PPT presentation

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Title: ENGI 1313 Mechanics I


1
ENGI 1313 Mechanics I
  • Lecture 26 3D Equilibrium of a Rigid Body

2
Schedule Change
  • Postponed Class
  • Friday Nov. 9
  • Two Options
  • Use review class Wednesday Nov. 28
  • Preferred option
  • Schedule time on Thursday Nov.15 or 22
  • Please Advise Class Representative of Preference

3
Lecture 26 Objective
  • to illustrate application of scalar and vector
    analysis for 3D rigid body equilibrium problems

4
Example 26-01
  • The pipe assembly supports the vertical loads
    shown. Determine the components of reaction at
    the ball-and-socket joint A and the tension in
    the supporting cables BC and BD.

5
Example 26-01 (cont.)
  • Draw FBD

Due to symmetry TBC TBD
6
Example 26-01 (cont.)
  • What are the First Steps?
  • Define Cartesian coordinate system
  • Resolve forces
  • Scalar notation?
  • Vector notation?

F1 3 kN
F2 4 kN
7
Example 26-01 (cont.)
  • Cable Tension Forces
  • Position vectors
  • Unit vectors

F1 3 kN
F2 4 kN
8
Example 26-01 (cont.)
  • Ball-and-Socket Reaction Forces
  • Unit vectors

F1 3 kN
F2 4 kN
9
Example 26-01 (cont.)
  • What Equilibrium Equation Should be Used?
  • ?Mo 0
  • Why?
  • Find moment arm vectors

F1 3 kN
F2 4 kN
10
Example 26-01 (cont.)
  • Moment Equation

Due to symmetry TBC TBD
F1 3 kN
F2 4 kN
11
Example 26-01 (cont.)
  • Moment Equation

F1 3 kN
F2 4 kN
12
Example 26-01 (cont.)
  • Force Equilibrium

F1 3 kN
F2 4 kN
13
Example 26-01 (cont.)
  • Force Equilibrium

F1 3 kN
F2 4 kN
14
Example 26-01 (cont.)
  • Force Equilibrium

F1 3 kN
F2 4 kN
15
Example 26-02
  • The silo has a weight of 3500 lb and a center of
    gravity at G. Determine the vertical component of
    force that each of the three struts at A, B, and
    C exerts on the silo if it is subjected to a
    resultant wind loading of 250 lb which acts in
    the direction shown.

16
Example 26-02 (cont.)
  • Establish Cartesian Coordinate System
  • Draw FBD

W 3500 lb
F 250lb
Bz
Cz
Az
17
Example 26-02 (cont.)
  • What Equilibrium Equation Should be Used?
  • Three equations to solve for three unknown
    vertical support reactions

W 3500 lb
F 250lb
Bz
Cz
Az
18
Example 26-02 (cont.)
  • Vertical Forces

W 3500 lb
F 250lb
Bz
Cz
Az
19
Example 26-02 (cont.)
  • Moment About x-axis

W 3500 lb
F 250lb
Bz
Cz
Az
20
Example 26-02 (cont.)
  • Moment About y-axis

W 3500 lb
F 250lb
Bz
Cz
Az
21
Example 26-02 (cont.)
  • System of Equations
  • Gaussian elimination

W 3500 lb
F 250lb
Bz
Cz
Az
22
Example 26-02 (cont.)
  • System of Equations
  • Gaussian elimination

W 3500 lb
F 250lb
Bz
Cz
Az
23
References
  • Hibbeler (2007)
  • http//wps.prenhall.com/esm_hibbeler_engmech_1
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